In the improvement of manufacturing processes and products it is often necessary to employ empirical methods or techniques. In most basic terms, this typically involves observing the effects of variables in a product or process and using the information observed from those effects to adjust or manipulate the variables, resulting in an improved or satisfactory product or process. However, where there are many variables with a multitude of possible effects on the process or product, arriving at improvements is more difficult.
Industrial methods of design and analysis of experiments have been developed to assist in transforming data and improving manufacturing processes. However, in practical applications, field experience has shown that existing methods do not yield adequate solutions. There is a need for a simple and easy to use method that transforms experimental field data into more revealing and practical information that can be used to improve processes and products.
The present invention provides a method of manufacturing or improving a manufacturing process. In addition, the method can be applied in the design of a manufacturing process or product.
In one embodiment described herein, a full factorial experiment is conducted with a plurality of process variables with each of the variables being tested at a plurality of settings, in a plurality of combinations of settings. Measurements of the response of the process for each combination of level settings are recorded.
The responses of the full factorial experiment are used to calculate individual contrasts for each process variable and each interaction among the process variables. The individual contrasts are each displayed at a particular location in a document, or other form of display, corresponding to a particular notation.
The individual contrasts of each process variable and each interaction are added to generate separate contrast sums which are also displayed in the document. In addition, effects estimates for each of the contrast sums are displayed.
Contrast sums are identified that are greater than at least one of the other contrast sums by a factor of about 2. If the contrast sum is that of an interaction effect between a plurality of process variables, the interaction is verified by referring to the document. The document provides information as to whether both variables of the interaction must be set at the levels of the interaction to impart an effect substantially equal to the effect of the interaction.
Furthermore, when at least two trials for the full factorial experiment are conducted, replicate effects can be generated. The document can be used to generate replicate effects wherein at least one hypothetical additional process variable is assumed and one set of the trial responses are substituted as responses for the hypothetical variable at one of two levels. Individual contrasts for the hypothetical variable are calculated, including the interaction contrasts thereof, to generate replicate effects.
Contrast sums are identified that are both greater than the next largest contrast sum by a factor of 2, as well as greater than all replicate effects calculated. Of the identified contrast sums, the significance of the contrasts, or associated effects, can be tested using an end count method.
The raw information from the process is thus transformed into information regarding the xe2x80x9csignificant effectsxe2x80x9d of level settings of the process variables. The level settings of the process can be adjusted to impart the xe2x80x9csignificant effectsxe2x80x9d to the process, or to avoid them, depending on whether the effects shift the process in the direction of an improvement.